The simplest type of de-esser is basically a compressor with an equalizer in the sidechain; the EQ makes the compressor more “sensitive” to high frequencies, so that it attenuates the high end of your audio signal to reduce the level of the “esses.” This kind of “wideband” de-essing is, of course, very effective — it’s been used with great results on countless recordings and live performance — but it can sometimes result in tonal artifacts in other audible frequencies besides the high end. In a split-band de-esser, such as the Waves Renaissance DeEsser plug-in (which offers both wideband and split de-esser modes), the frequency range is divided so that only the high frequencies are sent through the sidechain for attenuation, which results in fewer artifacts in the rest of the signal.
Which is best? It depends on your application and what your ears want to hear.